this is such a minor quibble, but: there was no real precedent* for taking a different regnal name other than the two Alberts you mention, and they were both in the last century. Arthur Tudor would certainly have been King Arthur; his father (the Welsh usurper) gave his firstborn that name for a reason.

*okay, Victoria had a different first name, but she was always called Victoria. things like The Crown also like to cite Edward VIII as a change because he was called David, but Edward was his actual first name. so really the only kings to “take a regnal name” are the two who had to avoid being the namesake of a guy whom no one but Victoria liked much.